Python PyTorch cumulative_trapezoid用法及代碼示例

本文簡要介紹python語言中 torch.cumulative_trapezoid 的用法。

用法:

torch.cumulative_trapezoid(y, x=None, *, dx=None, dim=- 1) → Tensor

參數：

• y(Tensor) -計算梯形規則時使用的值。

• x(Tensor) -如果指定，則定義上麵指定的值之間的間距。

關鍵字參數：

• dx(float) -值之間的恒定間距。如果 x 或 dx 均未指定，則默認為 1。有效地將結果乘以其值。

• dim(int) -計算梯形規則的維度。默認情況下最後一個(最裏麵的)維度。

沿著 dim 累積計算 trapezoidal rule 。默認情況下，元素之間的間距假定為 1，但 dx 可用於指定不同的常量間距，並且 x 可用於指定沿 dim 的任意間距。

更多詳情，請閱讀 torch.trapezoid() 。 torch.trapezoid() 與此函數之間的區別在於， torch.trapezoid() 為每個積分返回一個值，而此函數為積分中的每個間距返回一個累積值。這類似於.sum 如何返回一個值，而.cumsum 返回一個累積和。

例子：

>>> # Cumulatively computes the trapezoidal rule in 1D, spacing is implicitly 1.
>>> y = torch.tensor([1, 5, 10])
>>> torch.cumulative_trapezoid(y)
tensor([3., 10.5])

>>> # Computes the same trapezoidal rule directly up to each element to verify
>>> (1 + 5) / 2
3.0
>>> (1 + 10 + 10) / 2
10.5

>>> # Cumulatively computes the trapezoidal rule in 1D with constant spacing of 2
>>> # NOTE: the result is the same as before, but multiplied by 2
>>> torch.cumulative_trapezoid(y, dx=2)
tensor([6., 21.])

>>> # Cumulatively computes the trapezoidal rule in 1D with arbitrary spacing
>>> x = torch.tensor([1, 3, 6])
>>> torch.cumulative_trapezoid(y, x)
tensor([6., 28.5])

>>> # Computes the same trapezoidal rule directly up to each element to verify
>>> ((3 - 1) * (1 + 5)) / 2
6.0
>>> ((3 - 1) * (1 + 5) + (6 - 3) * (5 + 10)) / 2
28.5

>>> # Cumulatively computes the trapezoidal rule for each row of a 3x3 matrix
>>> y = torch.arange(9).reshape(3, 3)
tensor([[0, 1, 2],
        [3, 4, 5],
        [6, 7, 8]])
>>> torch.cumulative_trapezoid(y)
tensor([[ 0.5,  2.],
        [ 3.5,  8.],
        [ 6.5, 14.]])

>>> # Cumulatively computes the trapezoidal rule for each column of the matrix
>>> torch.cumulative_trapezoid(y, dim=0)
tensor([[ 1.5,  2.5,  3.5],
        [ 6.0,  8.0, 10.0]])

>>> # Cumulatively computes the trapezoidal rule for each row of a 3x3 ones matrix
>>> #   with the same arbitrary spacing
>>> y = torch.ones(3, 3)
>>> x = torch.tensor([1, 3, 6])
>>> torch.cumulative_trapezoid(y, x)
tensor([[2., 5.],
        [2., 5.],
        [2., 5.]])

>>> # Cumulatively computes the trapezoidal rule for each row of a 3x3 ones matrix
>>> #   with different arbitrary spacing per row
>>> y = torch.ones(3, 3)
>>> x = torch.tensor([[1, 2, 3], [1, 3, 5], [1, 4, 7]])
>>> torch.cumulative_trapezoid(y, x)
tensor([[1., 2.],
        [2., 4.],
        [3., 6.]])